Short answer: the treatment was different in some ways, but the racism was still very prolific and the collapse of communism left Roma in an even worse state in terms of economic possibilities, health, etc.

The Soviet Union was very much in the camp of forced assimilation of Roma. This included putting them in permanent housing (the quality of which obviously varied between countries and communities), providing jobs, and giving access to public services. Most of these jobs were in agriculture, factories, and labor. Anecdotally, Roma could practice some of their traditional and other trades--I'm thinking specifically about the memoir American Gypsy by Oksana Marafioti, which gives a very intimate glimpse of her childhood in 1980s Russia as a mixed Romani-Armenian girl, as her extended Roma family was part of a traveling Romani music group--but these also had to conform to Soviet culture in order to function safely. (In Marafioti's case, the rampant corruption and being able to offer bribes gave her family a lot of advantages most Roma didn't have.) Ronald Lee, a Roma activist and scholar, compares the situation of Roma under communism as a parallel to the situation of indigenous peoples in Canada, in that they came to rely on and were at the mercy of the State for basic necessities. (You can read an article he wrote about Roma under communism here )

Even with forced assimilation efforts, Roma were still never considered to be "real" Russians/Bulgarians/etc. Racism remained rampant. In Romania there are deep-set prejudices you can trace back to the chattel slavery of Roma in the nineteenth century. On the state level, Roma women were often sterilized without their knowledge or consent. This issue is only beginning to gain insight and traction, but this practice was rampant in Czechoslovakia and Hungary.

In theory, literacy rates should have improved due to the efforts to place Roma children in state-run schools, but the results are a mixed success. Ronald Lee states that Roma did indeed benefit and were able to integrate into higher-education positions such as doctors and engineers. However, as he points out, many of the Roma who were supposed to be educated in this time are functionally illiterate. Reports for the European Roma Right Center and personal testimonies point to sub-par education of Roma and racist treatment by staff and students. Bullying of Roma students was, and is, absolutely merciless. Educated Roma in both Europe and the United States recount being pelted with rocks by students, being punished by teachers for minor infractions (including some bigoted sentiments about "giving the evil eye" and "witchcraft"), and basically being treated like an outsider the second someone knew they were Romani.

A unique glimpse at efforts to educate Roma children in Czechoslovakia can be seen in the Czech documentary Buried Letters, which follows the former students of an experimental boarding school designed for Roma. If this sounds at all familiar to the indigenous American/Canadian experience... you're not far off. The former students did indeed get a good education, enjoyed their experience, and became successful adults in the Czech Republic. The cost was that the state totally cut them off from their families, destroyed their connections to their communities and culture, and basically made it so that they could only integrate back into the wider Czech society.

Today there are still a ton of problems in how European countries treat Romani pupils. Czech schools literally segregate Roma students from non-Roma students, and there are reports by the ERRC and from students all across Europe (including England) that Roma kids are default placed in the "special education" classes with the assumption that they are inherently mentally challenged. One English Roma dude on Reddit actually talked about his experience with it in an AskReddit thread.

The "socialist" (I'm assuming Nordic countries?) treatment of Roma was only marginally better as far as I'm aware, thanks in part to the efforts of a female Romani activist named Katarina Taikon. I'm much less familiar with the Kale/Roma living in Nordic countries, but a few leading Roma have expressed that they feel fortunate in comparison to Roma in the rest of Europe.

Regarding the lines of the song, this goes to an issue that's true of every country Roma have lived in: nowhere wanted "gypsies" to exist. There have been anti-gypsy laws in virtually every country where Roma have existed (including America and Canada). From the Roma perspective, there is absolutely zero reason to believe any efforts to "help" them will actually help them. Both in the past and in the present, being on any "official" documentation is seen as inherently dangerous for a lot of Roma (see: Italy and France's regular raids of Roma camps, attempts at deportation). The only way to stay safe for a lot of Roma is to either pretend you're not Roma, or if you can't do that, band together with your community. This creates some of its own internal issues, but that's something better to hear from actual Roma.